I always thought it was from the beginning of the orbit, but I never tested it formally. Sometimes I have had aircraft RTB unexpectedly instead of hanging out on an ASW/ANTISHIP waypoint. I am pretty sure I tried putting an intermediate WP between the ingress and ACTION point but now I cant remember. Maybe the counter did start when they turned toward the WP and expired when they got there??? Usually it seems more like they countdown after arrival, though...